This volume consists of 24 papers submitted for publication by the invited speakers of the IFIP International Conference on Stochastic Partial Differential Equations and their Applications. While most of them are research papers, however, a few surveys written by experts are also included. The aim of the conference was to bring together mathematicians, physicists and engineers representing academic as well as industrial fields, who were interested in the theory and applications of SPDE’s, a rapidly developing areas at the junction of several sciences. The main topics for discussion at the conference were non-linear SPDE’s and Markov property for random fields, modern stochastic calculus, numerical and asymptotic methods for SPDE’s, applications of SPDE’s with emphasis on non-linear filtering, and stochastic control and statistical fluid dynamics.